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At what point should the origin be shifted if the coordinates
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At what point should the origin be shifted if the coordinates of a point become

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An ellipse is drawn by taking a diameter of the circle as its semiminor axis and a diameter of the circle as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

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The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 unit on the x-and y-axis respectively. If the eccentricity of all such ellipses is 1./2 then find the locus of the focus.

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The locus of the foot of perpendicular drawn from the centre of the ellipse on any tangent to it is

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The ellipse is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

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Question Text
At what point should the origin be shifted if the coordinates of a point become